Prediction of propeller noise spectra

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ARCHIEF

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SPONSOR: DET NORSKE VERITAS

Ref.: PAPER 1/2 - SESSION 4

1.ab. y.

Scheepsbpuwkm

Technische

HO9dQOL

DeUI

SYMPOSIUM ON

"HYDRODYNAMICS OF SHIP AND OFFSHORE PROPULSION SYSTEMS"

H0VIK OUTSIDE OSLO, MARCH 20. - 25., 1977

"PREDICTION OF PROPELLER NOISE SPECTRA"

By

O. Björheden and L. Aström

KMW

tI AU SIAL)S MLKANSKA WLRKSIAD

Symposium on

Hydrodynamics of Ship

and Offshore Propulsion Systems

March 20-25, 1977

The New Ventas Centre, Hvik, Norway

PREDICTION OF PROPELLER NOISE SPECTRA

by

O. Björhedan and L.Iström

AB Karlatads Mekaniska Werkstad, Sweden

Abstract

In modern ships, propeller-induced noise has become an increasingly important matter to be dealt

with by

naval architects, project engineers and pro-peller manufacturers. In this paper a tentative method of estimating the propeller-induced noise onboard ships, on basis of model scale measurements,

is discussed. Some results from model and full scale noise measurements are presented as well.

Fig. i

AH KAHL !ADS ML KANISKA WEHKSTAD

Introduction

The development at sea towards more and more advanced ships together with the demands from the crews for a better working and living environment emphasizes the need for more research in the field of ship-board noise in general and

propeller-generated noise in particular. This concerns methods for predictions as well as possible means for reducing

noise levels.

The two principal sources of noise onboard. a

modern ship are the machinery including its auxiliary equipment and the propellers. Of course there are other noise sources which create problems, e.g. the air conditioning system, but in general the knowledge about these sources is well developed and the

possibi-lities of reducing the noise from same are good, though

it may involve additional costs.

A.s a rule, the machinery noise is dominating in

the upper parts of the ship, while the propeller-generated noise Is noticed in the lower aft parts. Considering existing as well as notified new noise requirements for ships, it may be concluded that attention must be paid not only to the ìachinery but

also to the propeller as a noise source. In figure 1, sound pressure levels obtained in unfitted steel rooms above the propeller on a number of vessels are shown.

-2-A KAIt:; At ; MI KANISKA WI HKS AL)

With due conuidertion to transmission losses

iì

bulkheads

and decks the resulting levels must still be regarded as high when comparing with the proposed Jwedish requirements of 85 dB (A) in the engine room and 45 dB (A) in crew cabins [1]. When ambitions are

set this high, efforts must be focused on reducing

the noise at its source for practical as well as

economic reasons. In solving the problems a certain specialization by various suppliers of equipment is natural. However, the need for coordination and close cooperation between various parties involved such as e.g. the hull designer and the propeller

designer must be strongly emphasized.

In the present paper a tentative method of predicting full scale propeller-induced noise levels and corresponding hull plating velocity levels, based upon cavitation tunnel noise measurements, is presented.

The limiting of this study to the propeller, and adjacent hull plating, is justified with regard to

other investigations concerning the noise

trans-mission in ships which are in progress. Calculation methods utilizing the hull plating velocity level

as an input have been

developed,

e.g. by TNO in

Holland and SF in Cweden

/J.

-5-F i

g.

KMW

-4-t'H KARt STA[) M1IKANIKA WERKSTAD

2. Propeller-induced noise

Noise generated by propellers may be divided into two categories, one related to the turbulent flow over the propeller blade sections, the other related to cavitation, in the cavitating region,

the cavitation noise is entirely dominating and there-fore, on most propellers operating in the uneven

velocity field behind a ship's stern, the turbulent

flow noise may be disregarded.

The cavitation noise generation may be explained from the behaviour of a single cavitation bubble as

shown schematically in figure 2.

When the bubble is imploding a sharp acoustic pressure peak is built up as indicated in the figure. The process may be repeated a number of times due to elastic reflection. At a given ambient pressure each size of a bubble corresponds to a certain implosion velocity and thereby to a certain frequency of the generated noise. The influence from the ambient static pressure may intuitively be understood in such a way that an increased pressure resulting in steeper pressure gradients will accelerate the implosion and will thus increase the frequency as well as the

acoustic pressure. The noise generated by a cavitating propeller, i.e. the resulting noise from a spectrum of

KMW

tIit :Air

1I F\ANIKA VVI HK;IAI)

iirplodin0 cavitation bubbles of different sizes,

can be divided into:

lm«losi ori of blade tip and ru,t vortex

cavita-Lion ir the water or on the rudder.

Implosion of cavitation bubbles o sheet3 in the water or ori the propeller blade surface.

Rapid fluctuations of cavittiori sheets, bubbles

and vortices.

1ropeller - hull vortex cavitation.

Cavitation according to case a) and b) generates noise in the frequency range roughly between 400 Hz and

50 kHz depending on the character of imploding cavitation bubbles and sheets. In case c) low frequency noise is

tçenerated approximately between 100 and 400 Hz. Case d)

represents a more unusual type of cavitation appearing

for instance on tankers and hul.kers with high block

coefficients and regions of very high local wake

frac-tions between propeller and hull. This type of

cavita-tion generates a sudden and violent hammering on the

h u li.

lin figure

_3,

cavitation patterns and corresponding noise spectra for a few different working conditions of a model propeller tested in one of the KMI cavitation

tunnels are shown. From the figure it can be seen how

the type and extent of cavitation has affected the noise

\P= pressure ampI i tude (=density of water n=propeiler speed D = pro pe lier diameter index m= model scale index s=ship

KMW

-6-ALi KAFLI StAllS MLKANftKA WLIIKSIAD

The propeller-induced pressure pulses cari thus

be divided into low freqiency Impulses, having influence upon the ship's vibration performance, and high

frequency impulses, normally recognized as noise. The low frequency impulses refer to the propeller blade frequency and its harmonics up to about 100 Hz in full scale, which is approximately the lower limit for sounds of ordinary speaking level. The low frequency impulses have been exhaustively treated in the literature and the relation

r

x(n

X

D)

Is s s ¿\p

=AP

s in x (n X D )2 in in

seems to give an acceptable correlation, at least for the blade frequency pressure pulses. The low frequency pressure pulses will therefore be omitted

in the following sections.

5. Tentative method of estimating full scale

propeller noise spectra

A tentative method for estimating the full scale propeller noise spectra with the aid of model scale noise measurements has been developed at the

KMW Marine Laboratory in connection with an

investi-gation for the Swedish Ship Research Foundation

f].

An early version of the method has been practiced

Fig. 4

Fig. 5

KMW

-7-AB KAHL S1ADS MEKANISKA WERKSTAD

In figure 4, the various steps of measurements

and calculations are shown.

The problem can be split into two different

parts which have to be solved individually to constitute a complete solution. At first there is the problw of determining the propeller-induced sound pressure level outside the hull plating. Then there is the complicated

problem of determining the structure response and the sound transmission through the hull plating. In order

to clarify the description the proposed tentative

solutions are divided into two sections.

3.1 Estimation of the full scale sound 2ressure level

The different steps in determining the full scale sound pressure level in water are shown in

figure 5.

In connection with an investigation of a water jet propulsion unit a survey of the hydro-acoustic qualities of the KMW cavitation tunnels was performed in 1973. In order to overcome the problems with reverberation and absorption a special calibration was carried out aiming at establishing a transfer function to free field conditions. A noise transducer connected to a

KMW

Ab KAHl MKANISKA WEHKSTAD

random noise generator was placed at different stations in the cavitation tunnel test section and

the sound pressure levels were recorded with the

aid of a hydrophone located in its ordinary position in a water-filled steel box in one of the test

section observation windows as shown in figure 6.

Fig. 6

With the same measuring equipment a corresponding survey was conducted In a free field measuring station with the same frequency range and intensity as for

the cavitation tunnel tests. By comparing the sound pressure levels obtained the transfer function was

derived.

The same acoustic calibration was later on

carried out in Lhe smaller cavitation tunnel 171 at the

Swedish State ìhipbuilding Experimental Tank (SSPA) in Gothenburg. A comparison between results of noise measurements from cavitation tests with the one and same model propeller in the SSPA tunnel Ti and the

KfM tunnel T-32 is shown in figure 7.

Fig. 7

The average difference in sound pressure levels obtained at five different operating conditions with and without the free field correction applied is given in the diagram. With the free field correction applied

the agreement between the two cavitation tunnels is

considerably improved.

-AH KAU TAE) M ANft,KA WtRKSTAD

Preasure ju1se uieaurenients

The method used for measuring lo frequency

pressure fluctuations wi.Lh the aid of pressure gauges

fitted in the hull model (figure 8) can be utilized

also for noise recordings.

The applicability is limited by the natural frequency of the pressure gauges, which is normally

between i and 6 kHz depending on the design. In order

to facilitate comparisons between pressure gauge

recordings and hydrophone recordings, both must be

transferred to the one and. samE: reference distance.

Jince the pressure pulse measurements are

conducted in the acoustic near field the propeller

cannot be regarded as a point source. However,

assuming the acoustic centre to be located at a

certain position and applying some propagation law,

the recordings may be converted to an arbitrary reference distance. As a first attempt the acoustic centre has been placed at the propeller blade tip closest to the hull plating, assuming the normal

sf)herictl propagation law. The pressure gauge

recordings obtained for a fast twin screw ferry and

converted to 1 m distance according to the assumptions

above are given in figure 9 in comparison with the

corresponding hydrophone recordings. The curves give

-9-1(14W

A KARt A[I ML KANISKA WI HK31A[)

averaged vaiues of a lar'.e number of recordings for

oiie opera t ing corid i tion, Lije sc t ter between di fferent

recnr:Iiign being rather :mal1. The result seems to

juu ti fy the annumptions made arid a further verification

of Lue tree field correction applied Lo hydrophone

recordings in obtained a ueil.

Application of scalin methods

Two different scaling methods have been applied in order to determine the full scale sound pressure

level. The estimated full scale levels appear from figure 10 and 11, in comparison with the full scale sound prenure level measured onhoard the twin screw

ferry mentioned above.

f i r; . i (') .;

sirle by jde

The first scaling method refers to a certain

e:terìt to the work by Baiter

f5J,

but one additional parameter, namely the veloci ty, has been included.

The following reasoning forms the basis for the

relations derived:

The basic assumption is that of geometrical

aimilarit:! between the cavitation patterns in model

and full ncale. The assumption Imniies that the radius

of each individual cavitation bubble is proportional

D

to the scale factor )' and moreover, that the extent

and relative site distribution of cavitation bubbles

-lo-\E KAIU lAI); Mf KANI,KA WERKSÌAD

anti sheets is the same in model and full scale. 'rom

the assuiiìption follows that the number of bubbles

appearing on the propeller blade in a certain

angular position is the same in model and full scale. The next assumption is that the theory of scaling of the shock wave noise from a single

cavi-tation bubble implosion, as presented by Baiter, is valid for the entire distribution of bubbles and sheets present on a propeller blade. The

assumptions made so far imply that the frequencies of the generated noise are Inversely proportional to the scale factor ) whilst the sound pressure level is directly proportional to the same factor

as indicated in figure 11.

The next assumption concerns the influence from velocity. From previous investigations It is known that cavitation-induced sound pressure levels are proportional to the n:th power of the velocity, n being an exponent between 2 and 5. In reference

[6]

the influence from velocity has been studied for hydrofoil profiles at constant cavitation numbers

and exponents between 2.5 and 5 have been obtained.

The investigation concerns primarily different forms of sheet cavitation. In the KMW cavitation tunnels

limited investigations have been conducted concerning propeller models working at constant cavitation

-11--KMW

:i h AlU AI. M KANISKA w 1KSTA[)

number and different velocities, the cavitation pattern being mainly characterized by tip vortices. In these

investigations exponents between 2.3 and 4 were obtained.

In the proposed scaling method an exponent equal to 3 has been chosen for the velocity influence, which

completes a set of formulae according to figure 12.

Fig. 12

f f r equer icy

V=eharacterjstj c

velocity

The scaling method according to Levkovskii

_17]

is founded on theoretical grounds, the frequency and level relations being derived from dimension studies assuming geometrical similarity in cavitation pattern

between model and full scale. For a single cavitation bubble Levkovskji assumes a constant relation between the radiated sound energy and the total energy content and furthermore he assumes the sound energy radiated

to be decreasing exponentially with time.

Le'vkovskij's method can be summarized in two

equations according to figure 13.

Fig. 13 cavitation number = pu - Pv IJ p -external sta-u tic pressure P=vaPour presnure L -sound pres-sure level r-radial distance from acoustic centre

-12-KMW

-1-I\t I'AHI ,Ii\t) !'I KArJI\\ \ìVI KIAI)

Iron

i j

urns

i H t. can be seen that

agreement bLieen estimated and measured full saale noise levels is reasonable for both scaling methods

when applied, to this single case. Of course several

additional tests including model and full scale measurements are required before more definite

conclusions can be made.

The differences between estimated and measured levels may primarily be related to differences in the model and full scala cavitation patterns, i.e. the distribution of bubbles and sheets, but other

explanations are possible as well. The level difference due to velocity for instance may be depending on

frequency as indicated by some results in [6].

Estimation of the hull plating velocity level The coupling between the waterborne pressure pulses on one hand and the oscillations of the hull

plating on the other is a complex acoustic problem.

Attempts to simplify the problem by replacing the hull structure by a single plate exposed to zero incidence soundwaves In the mass-controlled frequency range lead to transmission losses, which are much too high. Obviously, no such simple model can be applied for the sound transmission with regard to a number of factors involved. In the real case, all angles

Fíg. i

KMW

AE3 KAALSADS MEKANISKA WERKSTAD

of Lncidence occur causing not only lateral

vibra-tions, but also bending and compression waves in

the hull structure. Moreover, stiffenings of the hull

plating in terms of frames and bulkheads complicate

the determination of the acoustic impedance as well

as transmission losses. New calculation methods,

based on statistical energy analysis, will probably

throw some light on the different aspects of the

problem in the future.

For a limited number of Shíp8 the sound pressure level outside the hull plating has been compared to the corresponding vibration level and some results are

shown in figure 14.

4

The different levels given in the diagram represent average values for a number of measuring points in the area above the propeller. The curves

show a similar tendency for the three ships investigated although there are differences between individual

measuring points on a single vessel, as appears from figure 15. The difference between various measuring

pointe is most likely related to differences in the acoustic impedance due to variations in the local

stiffness and mass density of the hull structure.

Thus, for instance measuring point no. 1 in figure 15

as located in a ballast tank close to a longitudinal

KMÑ

At KAHL .tAt) Mt KANIKA VVL tKflA[)

bulkhead, while measuring points 2 and 3 were located

in regions of ordinary frame structure.

Figs. 15 & 16, side by side

When estimating the hull plating velocity

level some sort of an average curve, such as the

one shown in figure 16, could eventually be used.

In a broader statistical material the influence

from plate thickness, frame distance etc. may

possibly be taken into account. For ordinary

project purposes a simple concept, such as the one

indicated above, may prove to be as accurate and

useful as more complete theoretical solutions in

the future.

5. Conclusions and recommendations

A tentat.ive methoi for prediction of

propeller-induced noise levels in ships on basis of model scale measurements has been outlined. The various steps of measurements and calculations may be summarized as

follows:

Measurement of the cavitation noise generated by the model propeller operating in a simulated wake

fi eid.

Transformation of the measured noise level to

free field conditions taking cavitation tunnel

reverberation etc. into account.

-15--Aß KAHSIADS MEKANISKA WEAKS1AD

Transformation of the corre.ted model noise level into full scale level with the aid of scaling equa t i on

-Estimation of the hull plating velocity level.

Upon d) follows calculation of the sound trans-mi3sjon in the ship hull structure, taking area of sound energy emitting surface, transmission losses

etc. into account.

The technique of measuring the model scale

noise level with the aid of hydrophone and pressure gauges as well as the principle for transformation of the same into free field conditions seem feasible

and to sorne extent vérified by the results obtained.

similar measurements ought to be performed also in other cavitation tunnels in order to establish further confidence in the method applied. Methods for acoustic calibration of cavitation tunnels as well as mea8uring

techniques ought to be standardized to the highest possible extent and comparative tests should be

arranged, e.g. within the ITTC.

As to the transformation of model scale noise levels into full scale, both methods applied hava given reasonable agreement between measured and pre-dicted levels for thí only ship studied so far. In

this field, however, more basic research is required regarding the nature of noise generated by different

AK KAKLSAD5 MLKANISKA WEFIKSTAD

typez; of cavitation as well as its dependence of

scale, velocity, ambient pressure etc. More research is also required concerning scale effects influencing the propeller cavitation as well as the ship hull wake

distribution. evera1 more coordinated full scale and model investigations must be performed to form the

basis for correlation studies.

As regards the acoustic coupling between water and hull, theoretical methods for determination of the hull plating velocity levels based upon statistical energy analysis and finite element technique are

likely to come in the future. Meanwhile, further full scale measurements of propeller-induced noise (pressure

pulses) and corresponding hull plating vibrations are

recommended in order to add further material to the

statistical method sketched above.

Ac k n ow le de me n t

The authors wish Lo express their gratitude to the Swedish ;hip Research Foundation and to the management of AB Karistads Mekaniska Werkstad for their kind permission to publish the results included in this study. Sincere thanks are also expressed to those among the staff of the KNW

Marine Laboratory who have participated in the investigations

and contributed to the preparation of this report.

-17-AI AIiI IAL) MI F'ANI;A WI IIKSIAI)

Re ferences

BERG, P.4., draft on Föreskrifter orn Ljudklimat

pá Svenska Fartyg (Directions on the Sound

Environment onboard Swedish Ships), to come into

force in 1976 by Sjöfartsverkets Centralförvaltning.

Ingemanssons Ingenjörsbyr AB, Gothenburg,

PM H-6744-D, 1976, 51 pp.

PLtJNT, J. Methods for Predicting Noise Levels in

Ships, Part

6.

The Swedish Ship Research Foundation, report no. 5309:37 (classified),

1975, 14 pp.

Noise Emission from Propellers. The Swedish Ship

Research Foundation, project 5511 (classified).

ALBRECHT, K. Propeller Cavitation Noise, Some

Investigations Carried Out at the KÌTI Marine

Laboratory. 3NANE New England Section, panel

discussion on Propeller Noise", 7th March, 1975.

BAITER, 11.-J. Aspects of Cavitation Noise.

Symposium on High Powered Propulsion of Large

Ships, Wageningen, lOth-l3th December, 1974.

BAKER, S.l. Measurements of Radiated Noise in Caltech High-Speed Water Tunnel. Part II: Radiated

Noise from Cavitating Hydrofoils. Graduate

Aero-nautical Laboratories, CIT, March, 1975.

7. LEVKOVSKII, V.L. Modelling of Cavitation Noise.

Soviet Physics-Acoustics 13(1968):3, pp. 337-339.

u-120

100

80

60

40

Sound pressure leveL

in dB re 210e Pa

in octave band

31.5

63

125

250 500 1000 2000 4000 8000 16000

-

f(Hz)

Fig.1.

Sound pressure

LeveL in room above

propeller.

Measured values for about

20 vessels.

4

3

2

i

o

o

1.O[

_radius

Acoustic

pres sure

-i

Bubble

'

I'

\

/

'----r

i r w'

-2

-1

0

1

2

3

time

/

/

-13382.

Fig.2

Radial motion and sound pressure

for a vapour cavity which rebounds after

growing and coLlapsing.

Sound pressure

level in d: in

one--third

octav e

band

Fig.3

Relation between cavitation and sound

pressure

level

in a model test.

1 338 3.

Fig.4

Estimation of f uLL scale velocity Level

in the huLL plating with the aid of model

tests.

133 8t

Model noise measurements in

cavitation tunnel.

e

Transformation from cavitation tunnel

noise fleld to free water noise field.

Model to fuLL scale transformation

of noise with the aid of scaling laws.

Transformation of pressure pulse (noise)

level outside

hull

to a velocity level

Cavitation tunnel

Hydrophone and

pressure pulse

measuremen ts

Correcting to free

field

conditions and

i

m distance

Model. scol.e noise

Leve I

Application of

scaling methods

Hydrophone and

pressure pulse

recordings

Correcting to i m

distance

e

Full scaLe noise

level

le

Estimated full

scale noise level,

correlation

Fig.5

Estimation of full scale noise level

with the aid of model

tests.

noi se

transducer

hydrophone

dB

lo

-

olo

-L p100

free field level

L1

_-

LPM

third octave

band.

100 m

in

One-t hir d

band

and

random noise

g e n e r a to r

noi se

tr ansducer

pLexiglass

win d ow

octave

ana lyser

recorder

p-'

Lp1 = Lp100+ 40dB)

mea sur ing

sect on

water

filled

box

hydrophone

,pm

cavitation tunnel level

f L L L L L t L I t t

LI

I t J t t t

4f

I

JI

63 125

250

500 1000

2000

4000

8000

16000 31500

- 0

f

( Hz

Fig.6

Deduction of the transfer

function.

dB

re

2105Pa

in one-third

octave band

+ 10 o

- lo

- 20

- 30

o

£

£ mean difference between hydrophone

measurements

in

KMW

cavitation tunnel T-32

and SSPA

cavitation tunnel

T-1

without

correction.

mean difference with free field

correction applied.

Fig. 7

sêl i

I f

L 8 16

32H2 kH

Comparison of cavitation noise

from two cavitation tunneLs. Mean

vaLue

of five different conditions

with the same propelLer.

13387.

pressure transducers

Fig.8

Position of pressure transducers

¡n

model.. and ship.

dB re

21d5Pa

one-third octave band

150

140

90

80

70

Fig.9

C o

pressure puLses.

pressure pulses converted

to i m distance.

o hydrophone measurements

corrected to free field

conditions and 1m

distance.

a

125

250

500

1

2

1

8

₁₆

32Hz,kHz

Comparison between hydrophone and

pressure pulse measurements i n

cavitation tunnel.

i 3389

130

120

110

loo

dB

l50

1L0

130

120

110-loo

90..

80

Lp

re 21

one -the

octave

band

1m distance

63

125

250 500

1

2

L

8

16

32 Hz,kH

o

Sound pressure level as measured

in model scale.

Full scale sound pressure level estimated

with

the aid of KMW method.

D

Measured

full scale sound pressure level.

Fig.1O

Estimated full scale sound pressure level

in water compared with measured sound

pressure

level

for a twin screw ferry.

i i i i i t t i i i I - I 4 I 4 4 ê i t I I i $

KMW method

Lp

dB re 210

one-third

150

_octave

band

1 m distance

130

120

110

100

90

ê ê 4

144 4II4II $4144114141 4

63

125

250

500

1

2

4

8

16

32 Hz,kH2l

1 3391.

O A Sound pressure level as meosured

in model scale.

A. Full scale sound pressure level estimated

with the aid of

Levkovskii

method.

u

Measured full scale sound pressure level.

Fig. 11

Estimated

fulL scale sound pressure level

in water compared with measured sound

pressure

level

for a twin screw ferry.

dB

Sound

pressure

level

Predicted

full, scale noise level.

C

b

a

Model noise [eve(

frequency Hz

Frequency shift

_s/1m

1/A

Level difference due to scale 20 log A.

C.

Level difference

due to different

velocities 20 log

(Vs/Vm)3.

Fig.12. Scaling method according to

KMW hypothesis.

Predicted fuit scale noise Level

dB

Sound

pre s sure

t. e ve 1.

b

Model noise level

frequency Hz

1/2

Frequency shift fs/fmhIl(Ç/4)

Vs/Vm

Level difference

Lps_Lpm=2O

log

(Ç/«m)hI'2s/Vm) .(rj/r5)]

Fig. 13. Scaling method according to Levkovskii.

loo-

80-

60-40

Lp-Lv1 in dB

Lp re 210-e P

Lv1 re 5

10

rn/s

o 30000 tdw car carrier

+ 80000 tdw bulk carrier

o 3200 tdw

ferry

31.5

63

125

250

500 1000 2000 4000

f ( Hz )

Fig.14.Difference

Level

Lp-Lyi

Lp pressure pulse Level outside hull

Lv1 = velocity

level, of hulL plating.

LpLi ifl

one-third octave

band

dB

Lp re 21O

Pa

Lvi re. 5.108

m,s

loo

40

63

125

250

500

measuring point i

16

32 Hz1kHz

Lp = pressure puise level outside huit.

Li = velocity level of hull

plating.

Fig.15

Difference level Lp-Lvi for a number

of measuring points on a twin screw

ferry.

3

13395.

loo-

80-Lp re 2 105P

LpLvl in dB

_{Lvi re}

_5108m/s

f4

4

ê l4 4

i ê

f4

i f i I f

't

31.5

63

125

250

500 1000 2000 1.000

f (H2)

Lp=pressure pulse level outside hull.

LvlVe(OCity level of hull plating.

Fig.16 Pifference

level

Lp -Lvi

average

vaLue för three

ships.

13396.

P

i

t § s Fig. i Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 8 Fig. ₉ Fig. 10 Fig. 11

Sound pressure level in room above propeller.

Measured values for about 20 vessels.

Radial motion and sound pressure for a vapour cavity which rebounds after growing and collapsing.

Relation between cavitation and so.u2d pressure

level in a model test.

Estimation of full scale velocity level in the

hull plating with the aid of model tests.

Estimation of full scale noise level with the

aid of model tests.

Deduction of the transfer function.

Comparison of cavitation noise from two cavitation tunnels. Mean value of five different conditions with

the same propeller.

Position of pressure transducers in model and ship.

Comparison between hydrophone and. pressure pulse

measurements in cavitation tunnel.

Estimated full scale sound pressure level in water compared with measured sound pressure level for a twin screw ferry. KI!IW method.

Estimated full scale sound pressure level in water compared with measured sound pressure level for

a twin screw ferry. Levkovskii method.

j

KNW

1

-AB KARLSTADS MEKANISKA WERKSTAD

Figure captions

Fig. 6

§ Fig. 2 Fig. 13 Fig. 14 Fig. 15 Pig. 16

Scaling method according to KTP1 hypothesis.

Scaling method according to Levkovskii.

Difference level L - L

p

Difference level L - L for a number of measuring

p V1

points on a twin screw ferry.

Difference level L - L average value for three

p

ships.

I(NW